Bring a large pot of salted water to a boil over high heat. Add the live lobsters and cook for 8-10 minutes until they turn bright red. Remove with tongs and let cool before extracting the meat.

Melt 2 tablespoons of butter in a large skillet over medium heat. Sauté finely chopped shallots for 3-4 minutes until translucent. Add 1 cup of sliced mushrooms and cook until tender, about 5 minutes.

Pour ½ cup of dry white wine into the skillet. Simmer for 3-4 minutes, then stir in 1 cup of heavy cream, cooking for an additional 3 minutes until thickened.

Chop the lobster meat and fold into the sauce with 1 teaspoon of paprika and half of the Parmesan cheese. Season with salt and pepper and warm through for 2-3 minutes.

Spoon the lobster mixture back into the shells, sprinkle with remaining Parmesan, and broil on high for 3-5 minutes until golden brown.

Serve immediately while hot, ideally with a side salad or crusty bread.